Question

Why does the resistance of a conductor increase with an increase in temperature?

Answer 1

Hint: In order to answer the above question, we will know some basics about the term resistance and conductor. We will find the relation between resistance and conductor. Finally, we will come to a conclusion regarding the temperature dependence of resistivity in a conductor.

Complete step by step solution:
First of all we will understand the terms resistance and conductors.
RESISTANCE:
The opposition to current flow in an electrical circuit is measured by resistance (also known as ohmic resistance or electrical resistance). The Greek letter omega ($\Omega $) is used to represent resistance in ohms.
There would be an electric current flowing through a material when a voltage is applied through it. The current across the material is directly proportional to the applied voltage through it. Resistance is the proportionality constant. As a result, resistance is defined as the proportion of applied voltage to current flowing through a material.
$V=IR$
Where $V$ represents voltage, $I$represents current, and $R$represents resistance.

CONDUCTORS:
Certain materials, mostly metallic substances, have a very low resistance to current passing through them. Conductors, or more specifically electrical conductors, are the name given to these substances. Silver is an excellent conductor of electricity, but its high cost prevents it from being commonly used in electrical systems. Aluminium is a fine conductor, and because of its low cost and wide availability, it is a widely used conductor. Copper is another strong conductor that is widely used in various electronics and electrical circuits. It is a better conductor than aluminium, but it is also more expensive.

As we know that the conductors have free electrons on their surfaces, allowing current to flow freely. Conductors are able to conduct electricity because of this. Or we can also say that the energy gap or the band gap between the valence band and the conduction band is very small or overlaps each other in conductors and hence the electron transfer from the valence band to the conduction band is very easy and takes place spontaneously. Therefore, we can say that the conductors have a very low resistivity.
When the temperature of a metallic conductor rises, so does the kinetic energy of the conductor's electrons, the free electrons on the surface of a conductor gains this energy and starts flowing here and there. The flow of electrons is so intense, that they collide with each other resulting in further obstruction to the moving electrons and hence the current. As a result, the resistance rises as more obstruction is placed in the way of the moving electrons.
Therefore, we can say that the resistivity is directly proportional to the temperature in case of conductors.

Note:
It is very important to note that the temperature dependency of the semi-conductors and insulators is totally different to that of a conductor. In semiconductors and insulators, the resistance is inversely proportional to the temperature and hence we can say that in semiconductors and insulators, the resistance decreases with increase in temperature.